As \(n\)  and \(\gamma \)  increase the generalised posterior precision increases and the distribution converges to a point mass at \(\hat{\theta }_{TW}\) . Note that under a uniform prior distribution (\(\tau ^2 \rightarrow \infty \) ), the generalised posterior mode would be equal to the maximum generalised likelihood estimate. However, in this case the posterior mode is shrunk toward the prior mode of zero. Although multiplying the loss by a constant \(\gamma \)  will not change the minimiser, \(\hat{\theta }_{TW}\) , it clearly has a significant effect on the generalised posterior distribution. The choice of \(\gamma \)  controls the relative weight of information from the responses and from the prior distribution. [1]} discuss various strategies for automatic adjustment of the generalised posterior distribution including 1) specifying \(\gamma \)  so that the responses provide a factor of \(n\)  times more information than the prior; 2) allowing \(\gamma \)  to be unknown with its own loss and prior so the resulting generalised posterior is more robust to its misspecification and 3) choosing \(\gamma \)  so that the generalised posterior has the desired frequentist properties.
